A derivative is an investment, often in the form of a financial instrument such as an agreement representing shares, from which payoffs over time are derived from the performance of assets (such as commodities, shares or bonds), interest rates, exchange rates or indices (such as a stock market index, consumer price index (CPI) or an index of weather conditions). The performance of the asset, interest rate, exchange rate or index can determine the amount or timing of the payoffs, or both. All details regarding the amount and timing of the payoff as well as the underlying assets, i.e. the value of the financial instrument, are subject to an agreement defining these details. Portions of the agreement apply to all financial instruments issued thereunder while portions of the agreement specific to the particular financial instrument, i.e. number of shares and beginning value of the underlying asset, are fully defined in the financial instrument. The main types of derivatives are futures, forwards, options and swaps. A swap is where a first party exchanges their future cash flow for the future cash flow of a second party.
In the field of derivatives, a popular form of swap is the interest rate swap (“IRS”), in which one party exchanges a stream of interest for another party's interest stream. IRSs are normally ‘fixed against floating’, i.e. the first party exchanges cash flow related to a loan made at a fixed interest rate for cash flow to a second party related to a loan at a variable rate of interest. IRSs can also be ‘fixed against fixed’ or ‘floating against floating’ rate swaps. The IRS agreement is entered into between two counterparties under which each agrees to make periodic payment to the other for an agreed period of time based upon a notional amount of principal. The principal amount is notional because there is no need to exchange actual amounts of principal in a single currency transaction. A notional amount of principal is required in order to compute the actual cash amounts that will be periodically exchanged.
IRSs are often used by companies to alter their exposure to interest-rate fluctuations, by swapping fixed-rate obligations for floating rate obligations, or swapping floating rate obligations for fixed-rate obligations. By swapping interest rates, a company is able to synthetically alter their interest rate exposures and bring them in line with management's appetite for interest rate risk.
Usually, one “leg” of an IRS involves quantities that are known in advance, known as the “fixed leg”, the other leg involves quantities that are not known in advance, known as the “floating leg”. The floating leg, i.e. the floating interest rate obligation, must therefore be “reset” against an agreed reference rate, which will become known at some point before payment or settlement takes place. For instance the parties might agree to pay 50 basis points (0.5%) over the LIBOR measured on the 1st trading day of every 3rd month. The payment schedule is often, but not always, timed to coincide with the resets. London Interbank Offered Rate (“LIBOR”) is a reference rate that varies daily based on the interest rates at which banks offer to lend unsecured funds to other banks in the London wholesale (or “interbank”) money market. Ideally, the determination of the reference rate must be outside the control of the counterparties, otherwise a conflict of interest will arise. Typically, the reference rate is some figure made publicly available by a third party information vendor, or by government agencies, e.g. LIBOR. Once a component of the floating leg is fixed (or “reset”), the fixed and floating components can be swapped or settled (typically one or two days after the fixing date).
Party F (for “fixed rate”) holds a fixed-rate loan, party V (for “variable rate”) holds a variable-rate loan. In a swap, F will make the payments on V's loan and vice versa. There is no change in the balance sheets of either party, because the principal, i.e. the underlying ‘notional’ amounts, offset one another and stay where they were. In other words, what is called a $1 billion swap typically involves amounts much smaller than $1 billion. Thus, Party V agrees to pay Party F periodic interest rate payments of LIBOR+50 bps (bps=basis points=0.01%) in exchange Party F agrees to pay Party V periodic interest rate payments fixed at 3.00%. Note that there is no exchange of the principal amounts and that the interest rates are on a “notional” (i.e. imaginary) principal amount. Also note that the interest payments are settled in net. Thus, if LIBOR is 1.20% when payments are due then LIBOR+50 bps=1.70%; the fixed rate of 3.00% less this 1.70% means that Party V receives the ‘net’ of 1.30%. The fixed rate (3.00% in this example) is referred to as the swap rate. If the underlying notional amount were $1 billion and the revenue flow is calculated once annually, Party F would owe Party V $13,000,000. In the same example, if the net payment for the swap were calculated quarterly then Party F would owe Party V $ 3,250,000. This is because the interest rate is annualized and the term is one quarter of the year.
Trading an IRS is one of the more common forms of over-the-counter derivatives. It is the most widely used derivative in terms of its outstanding notional amount, but it is not standardized enough and does not have the properties to easily change hands in a way that will let it be traded through a futures exchange like an option or a futures contract. That is, even though the term ‘plain vanilla’ can be applied to the swap, variables in any given swap are different enough that standardization is very difficult. Such variables include the notional amount, the variable rate, the fixed rate, the swap/credit spread, the term (in years), risk of nonpayment by any single participant, currency etc. Thus, the liquidity of even the plainest of plain vanilla swaps is low.
The present value of a plain vanilla (i.e. straightforward) swap can be computed using standard methods of determining the present value of the components. Two things should be kept in mind when thinking about the ‘value’ of a particular swap. First, when the swap is entered into the value of the swap to either party is typically zero. That is, the fixed and/or variable interest rate is ‘set’ (taking all publicly available information into account), e.g. by varying the fixed rate or the bps added to LIBOR, such that the cash flow from F to V is equal to the cash flow from V to F for the entire term of the swap. A party is not going to enter into a swap such that the future value of the swap starts out as a liability. One exception is where Party F pays Party V to enter into a swap that is a liability, i.e. has a negative present value, to Party V. The payment from party F to party V is precisely the same as the liability of the swap to Party V. Second, some variability is going to be introduced over the life of the swap. Typically, this variability comes in the form of one leg of the swap being subject to a variable interest rate. Thus, the series of payments based on variable rates, from Party V, are determined at the agreed dates of each payment.
The most obvious difficulty to be overcome in attaching a present value to a swap would seem to be the fact that the future stream of floating rate payments is unknown. At the time the swap is entered into, only the actual payment rates of the fixed leg are known in the future. This is literally true because it is not known with certainty what the 6 month US dollar LIBOR rate will be in 12 months time or 18 months time. However, markets possess a considerable body of information about the relationship between interest rates and future periods of time. An estimation of the future rates affecting the floating leg can be derived from the yield curve, to be further discussed below.
There is a large and liquid market in interest bearing securities issued by governments. Liquid means that the price of a security is well known to all market participants and, thus, it is typically very easy to convert a “liquid” financial instrument into cash or vice versa by buying or selling that instrument. These securities pay interest on a periodic basis and are issued with a wide range of maturities. Principal on these government securities is repaid only at maturity and at any given point in time the market values these securities to yield whatever rate of interest is necessary to make the securities trade at their par value. It is possible, therefore, to plot a graph of the yields of such securities vs. their varying maturities. This graph is known generally as a yield curve, i.e. the relationship between future interest rates and time.
The classic example of a yield curve is the US Treasury yield curve, an example of which is shown in FIG. 1. Thus, yield curve 1 discloses that, at a particular point in time for which yield curve 1 is applicable, a 5 year U.S. government bond had a yield of approximately 4% and a 20 year bond had a yield of approximately 4.5%. For example, at a certain time of a particular day in November, 2005, all of the available data put together revealed that the ‘market’ believed that the yield of a 5 year U.S. bond was 4% and the yield of a 20 year U.S. bond was 4.5%. All of this data regarding the market was compiled in yield curve 1.
Another government security is the zero coupon bond. The zero coupon bond does not pay interest at periodic intervals. Instead it is issued at a discount from its par or face value but is redeemed at par, the accumulated discount which is then repaid representing compounded or “rolled-up” interest. A graph of the internal rate of return (IRR) of zero coupon bonds over a range of maturities is known as the zero coupon yield curve 2 in FIG. 2. FIG. 2 also shows the par yield curve 3.
Finally, at any time the market is prepared to quote an investor forward interest rates. If an investor wishes to place a sum of money on deposit for six months and reinvest that money after maturity for a further six months, then the market will quote today a rate at which the investor can re-invest his deposit in six months time. The six month forward deposit rate is not a ‘guess’; it is a mathematically derived rate which reflects an arbitrage relationship between current (or spot) interest rates and forward interest rates, i.e. the six month forward interest rate is the rate of interest which eliminates any arbitrage profit. The forward interest rate will leave the investor indifferent as to whether he invests for six months and then re-invests for a further six months at the six month forward interest rate or whether he invests for a twelve month period at today's twelve month deposit rate. FIG. 3 shows an example of the forward curve 4. FIG. 3 also shows a zero coupon yield curve 5 and a par bond yield curve 6.
Thus, the market possesses sufficient information concerning the yield generated by existing instruments over future periods of time. The market has the ability to calculate forward interest rates which will eliminate arbitrage profit with spot interest rates. All of this information is available from publicly available sources. Future floating rates of interest can be calculated, therefore, using the forward yield curve. This, however, is not sufficient to calculate the future payments due under the swap and, thus, the mark to market value of the swap at a given point in time.
As discussed above, the aggregate set of cashflows due under any swap is—at inception—zero. That is, the net present value of both the fixed rate stream of payments and the floating rate stream of payments in a fixed to floating IRS is zero and the net present value of the complete swap must be zero. Since the floating rate payments due under the swap can be calculated (as explained above) it follows that the fixed rate payments will be such that when they are deducted from the floating rate payments and the net cash flow for each period is discounted at the appropriate rate given by the zero coupon yield curve, the net present value of the swap will be zero. It might also be noted that the actual fixed rate produced by the above calculation represents the par coupon rate payable for that maturity if the stream of fixed rate payments due under the swap are viewed as being a hypothetical fixed rate security.
Each future variable rate payment is calculated using the forward rate, from the forward rate curve, for each respective payment date. A series of future cash flows is thus calculated. Each cash flow is discounted by the zero coupon rate for the date of the payment, calculated from the zero coupon yield curve data. Zero coupon rates are used because these rates are for bonds which pay only one cash flow. The IRS is therefore treated like a series of zero coupon bonds.
The fixed rate offered in the swap is the rate which values the fixed rate's payments at the same value as the variable rate payments using today's forward rates. Therefore, at the time the contract is entered into, there is no advantage to either party, and therefore the swap requires no upfront payment.
During the life of the swap the same valuation technique is used. Over time, many of the factors described above, including the yield curve, the zero coupon bond curve and the forward curve will have changed. In fact, these curves change continuously. Based on these changes, mark to market accounting for the swap will almost always reveal the swap to be an asset to one party and a liability to the other.
Reversing or terminating an IRS is often necessary or desirable. As discussed previously, the shape of the curves used to price the swap initially will change over time. We begin with the assumption that shortly after a swap there is an increase in forward interest rates, i.e. the forward yield curve steepens. Since the fixed rate payments due under the swap are fixed, this change in the prevailing interest rate environment will affect future payments made under the floating rate arm. This benefit will accrue to Party F and will represent a cost to the Party V. If the future net cash flows of the swap are computed from the latest forward yield curve and discounted at the appropriate new zero coupon rate for each future period, i.e. reflecting the current zero coupon yield curve, the positive net present value result reflects how the value of the swap to Party F has risen. Correspondingly, it demonstrates how the value of the swap to Party V has declined.
Using common financial terminology, this valuation of the swap may also be called “mark to market” of the IRS. If, having done this, the floating rate payer wishes to terminate the swap with the fixed rate payer's agreement, then the positive net present value (“mark to market”) figure we have calculated represents the termination payment that will have to be paid to the fixed rate payer. Alternatively, if the floating rate payer wishes to cancel the swap by entering into a reverse swap with a new counterparty for the remaining term of the original swap, the net present value figure represents the payment that the floating rate payer will have to make to the new counterparty in order for him to enter into a swap which precisely mirrors the terms and conditions of the original swap.
Some basic reasons for swap transactions will now be discussed. A company with excellent credit will pay less to borrow money under identical terms than a less creditworthy company. The extra paid by the less creditworthy company is referred to as a “credit quality spread”. This spread is typically greater in relation to fixed interest rate borrowings than it is for floating rate borrowings. This spread also typically increases with maturity. The swap party making fixed rate payments (Party F) in a swap is predominantly the less creditworthy participant. Companies can lower their costs of borrowing by using swaps in conjunction with credit quality spreads. IRSs are used by a wide range of banks, non-financial operating companies, insurance companies, mortgage companies, investment vehicles and trusts, government agencies and sovereign states for one or more of the following reasons: 1. To lower funding costs; 2. To hedge interest rate exposure; 3. To implement asset or liability management strategies; 4. To create types of investments not currently obtainable; 5. To obtain higher yields from investment assets; and 6. Speculation in relation to future movements in interest rates.
The advantages of IRSs include the following: 1. A floating-to-fixed swap increases the certainty of an Party V's future obligations; 2. swapping from fixed-to-floating rate may save Party V money if interest rates increase (conversely, if interest rates decrease, Party F will have the positive net cashflow); 3. swapping allows issuers to revise their debt profile to take advantage of current or expected future market conditions; and 4. IRSs are a financial tool that potentially can help issuers lower the amount of debt service.
Investors, for their own reasons, enter into transactions to buy or sell an IRS of a particular duration while simultaneously selling or buying an IRS of a longer duration. This activity, though of great value to the investor, is expensive as it includes IRS transaction brokerage fees and the IRS bid offer spread for two periods. Should that investor then wish to exit the trade, the same bid offer has to be crossed and transaction fees again paid. This method of trading is antiquated by nature if only by the exposure to losses in attempting to trade large amounts of two swap periods at the same time; as such, trades of this type lend themselves perfectly to an index eliminating such risks.
There is also a lack of a viable bench mark for which corporate bonds can be pegged. Although treasuries can be used, the spread activity is a more accurate barometer of interest movement when it comes to corporate lending.
To trade traditional IRS there are various costs incurred, including crossing the bid offer spread, cost of credit, and transaction/brokerage fees. In addition, unlike most notes or bonds where the maturity is fixed, the IRS market completes each transaction out of spot (2 working days forward of the trade date) and with the end date being the duration, i.e. 2, 5, 10, 30 years, should the trader wish to reverse her position at any time after the original trade date there is an obvious mismatch in the end date. This increases exposure and creates complications in back office management of positions which, in turn, increases possible trading errors. Should a trader wish to take advantage of the yield curve by executing 2 years and executing 10 years, in order to be properly duration weighted the trader has to complete a 2 year IRS having a notional amount of approximately $400 million for a notional amount of $100 million in the 10 year IRS. This creates liquidity risk because executing the required notional amount of 2 years is multiplicatively more difficult than executing the required notional amount of ten years. Liquidity risk as for instance should she trade the 10 year leg the subsequent volume required to complete the 2 year leg of the trade may not be available, or the reverse should she trade the 2 years once the volume is completed the 10 year price may have moved against the trader, both trading methods are cumbersome and can create unwanted positions these can be the most expensive of all costs associated with trading the IRS, as the traders options are limited to running the unwanted position in the hope that the curve trade can be completed or unwind the trade and cross the bid offer and absorb any price changes to reverse it.